surname names
Number Number
Paper
9FM0/02
Advanced
Marks
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebraic manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
• If pencil is u s ed for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes • at the top of this page with your name,
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– theremay be morespacethan you need.
You should show sufficient working to make your methods clear.
• Answers without working may not gain full credit.
InIfnoerxam
ctaatnisown
ers should be given to three significant figures unless otherwise stated.
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
There are 9 questions in this question paper. The total mark for this paper is 75.
T– huesemtahrisksasfoargeuaidceh aqsuteosthioow
n amreucshhotiwmneintobsrpaec nkedtos n each question.
Advice
• Read each question carefully before you start to answer it.
Try to answer every question. •
Check your answers if you have time at the end.
Turn over
P72795A
,1.
R
initial line
O
Figure 1
Figure 1 shows a sketch of the curve with polar equation
r 2 sinh θ cosh θ 0 θ π
The region R, shown shaded in Figure 1, is bounded by the initial line, the curve and the
line with equation θ = π
Use algebraic integration to determine the exact area of R giving your answer in the
form peq – r where p, q and r are real numbers to be found.
(4)
2
,Question 1 continued
(Total for Question 1 is 4 marks)
3
, 2. (a) Write down the Maclaurin series of ex, in ascending power of x, up to and including
the term in x3
(1)
(b) Hence, without differentiating, determine the Maclaurin series of
e(e – 1)
x
in ascending powers of x, up to and including the term in x3, giving each coefficient
in simplest form.
(5)
4
Number Number
Paper
9FM0/02
Advanced
Marks
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebraic manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
• If pencil is u s ed for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes • at the top of this page with your name,
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– theremay be morespacethan you need.
You should show sufficient working to make your methods clear.
• Answers without working may not gain full credit.
InIfnoerxam
ctaatnisown
ers should be given to three significant figures unless otherwise stated.
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
There are 9 questions in this question paper. The total mark for this paper is 75.
T– huesemtahrisksasfoargeuaidceh aqsuteosthioow
n amreucshhotiwmneintobsrpaec nkedtos n each question.
Advice
• Read each question carefully before you start to answer it.
Try to answer every question. •
Check your answers if you have time at the end.
Turn over
P72795A
,1.
R
initial line
O
Figure 1
Figure 1 shows a sketch of the curve with polar equation
r 2 sinh θ cosh θ 0 θ π
The region R, shown shaded in Figure 1, is bounded by the initial line, the curve and the
line with equation θ = π
Use algebraic integration to determine the exact area of R giving your answer in the
form peq – r where p, q and r are real numbers to be found.
(4)
2
,Question 1 continued
(Total for Question 1 is 4 marks)
3
, 2. (a) Write down the Maclaurin series of ex, in ascending power of x, up to and including
the term in x3
(1)
(b) Hence, without differentiating, determine the Maclaurin series of
e(e – 1)
x
in ascending powers of x, up to and including the term in x3, giving each coefficient
in simplest form.
(5)
4
